Multiple Object Tracking Using K-Shortest Paths Optimization

TLDR

Multi‑object tracking links per‑frame detections into trajectories, tolerating occasional missed detections while ignoring brief false positives, but the linking step becomes a hard optimization problem that greedy or sampling dynamic‑programming methods often fail to solve globally. This study reformulates the linking step as a constrained flow optimization, turning it into a convex problem. By exploiting the problem’s structure, the authors solve the convex flow with a fast k‑shortest‑paths algorithm. The resulting method is formally and algorithmically simpler than existing techniques and achieves excellent performance in two distinct application contexts.

Abstract

Multi-object tracking can be achieved by detecting objects in individual frames and then linking detections across frames. Such an approach can be made very robust to the occasional detection failure: If an object is not detected in a frame but is in previous and following ones, a correct trajectory will nevertheless be produced. By contrast, a false-positive detection in a few frames will be ignored. However, when dealing with a multiple target problem, the linking step results in a difficult optimization problem in the space of all possible families of trajectories. This is usually dealt with by sampling or greedy search based on variants of Dynamic Programming which can easily miss the global optimum. In this paper, we show that reformulating that step as a constrained flow optimization results in a convex problem. We take advantage of its particular structure to solve it using the k-shortest paths algorithm, which is very fast. This new approach is far simpler formally and algorithmically than existing techniques and lets us demonstrate excellent performance in two very different contexts.